Question

In order to create a tight fit between two metal parts, machinists sometimes make the interior part larger than the hole into which it will fit and then either cool the interior part or heat the exterior part until they fit together. Suppose an aluminum rod with diameter D1 (at 17.5 °C) is to be fit into a hole in a brass plate that has a diameter D1 = 22.000 mm (at 17.5 °C). The machinists can cool the rod to 83.5 K by immersing it in liquid nitrogen. What is the largest possible diameter that the rod can have at 17.5 °C and just fit into the hole if the rod is cooled to 83.5 K and the brass